Music, as composed and played in the western world, is almost universally based on the use of harmonically related notes, i.e., the notes are selected from groups of notes, the frequencies of which groups differ from each other by factors of two, i.e., an octave. The individual notes within each octave (in the western world) are commonly defined by a twelve-tone equal-tempered scale. In this scale, the adjacent notes are related by the twelfth root of two, and alternate notes are named C, D, E, F, G, A, and B (with C being the lowest note). The semi-tones between are termed “sharp” or “flat”. Conventionally, the octaves are numbered (1, 2, 3, etc.) such that the note A4 has a frequency of 440 Hz.
Stringed musical instruments, such as the upright bass, viola, violin, guitar, etc. each include a specified number of stretched strings, each of which produces one of the desired notes. The note produced by a particular string depends on a number of factors, including the mass of the string, its length, and the tension in the string. Different instruments are designed to produce particular notes. An upright bass, for example, usually has four strings, tuned to produce the notes E1, A1, D2, and G2. Other instruments have the same or a different number of strings, generally tuned to provide specific notes as appropriate to the type of instrument.
While instruments that are tuned in the historically customary manner can, and do, provide much pleasing music, sometimes a musician may wish that his or her instrument is capable of playing other notes. For example, if an upright bass player were able (during a performance) to retune the low E1 note to D1, more harmonic variations would be possible, which could enhance the musical performance. Or, if the upright bass tuning could be instantly changed to fifths (C1, G1, D2, A2—cello tuning for bass) from the standard fourths tuning (E1, A1, D2, G2—standard bass tuning), the instrument would have substantially increased versatility.
There have been a number of attempts to produce devices that provide the foregoing functionality, but they generally have not been completely satisfactory. In many cases, it has not been easy or convenient to switch from one tuning to another during a performance, so that the advantage of the extra notes potentially available has not been easily accessible. In other cases, significant modification of the basic instrument is required, which is resisted by most musicians. Other problems have also arisen.